A consistent clustering-based approach to estimating the number of change-points in highly dependent time-series
This work addresses a fundamental limitation in change-point detection for time-series analysis, offering a theoretical solution with practical implications in fields like finance or signal processing, though it is incremental as it builds on existing clustering methods with an added constraint.
The paper tackles the problem of consistently estimating the number of change-points in highly dependent time-series data generated by unknown stationary ergodic processes, showing that a clustering-based approach can achieve this under the constraint that the number of underlying process distributions is known, with asymptotic consistency proven and empirical evaluations provided.
The problem of change-point estimation is considered under a general framework where the data are generated by unknown stationary ergodic process distributions. In this context, the consistent estimation of the number of change-points is provably impossible. However, it is shown that a consistent clustering method may be used to estimate the number of change points, under the additional constraint that the correct number of process distributions that generate the data is provided. This additional parameter has a natural interpretation in many real-world applications. An algorithm is proposed that estimates the number of change-points and locates the changes. The proposed algorithm is shown to be asymptotically consistent; its empirical evaluations are provided.